Abstract Research on student understanding of eigentheory in linear algebra has expanded recently, yet few studies address student understanding of the Characteristic Equation. In this study, we explore quantum physics students’ conceptual and procedural knowledge of deriving and using the Characteristic Equation. We developed the Conceptual and Procedural Knowledge framework for classifying the quality of students’ conceptual and procedural knowledge of both deriving and using the Characteristic Equation along a continuum. Most students exhibited deeper conceptual and procedural knowledge of using the Characteristic Equation than of deriving the Characteristic Equation. Furthermore, most students demonstrated deeper procedural knowledge than conceptual knowledge of deriving the Characteristic Equation. Most students demonstrated conceptual knowledge that was as deep or deeper than their procedural knowledge of using the Characteristic Equation. Examples of student work are provided, including descriptions of student work exhibiting rich knowledge of the characteristic equation. Implications for instruction and future research are discussed.

中文翻译：

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表征量子物理学学生对特征方程的概念和程序知识

摘要 最近，关于学生对线性代数特征论理解的研究有所扩大，但很少有研究涉及学生对特征方程的理解。在这项研究中，我们探索了量子物理学学生在推导和使用特征方程方面的概念和程序知识。我们开发了概念和程序知识框架，用于对学生在推导和使用特征方程方面的概念和程序知识的质量进行分类。大多数学生展示了使用特征方程比推导特征方程更深的概念和程序知识。此外，大多数学生展示了比推导特征方程的概念知识更深入的程序知识。大多数学生展示的概念知识与他们使用特征方程的程序知识一样深或更深。提供了学生作业的例子，包括展示丰富的特征方程知识的学生作业的描述。讨论了对教学和未来研究的影响。